A long-sought goal in the field of optics has been the ability to receive high-resolution images (i.e., two-dimensional information) that have been transmitted through a distorting medium, such as the atmosphere or a multimode optical fiber. Nonlinear optical techniques have been developed for the correction of images transmitted through "thin" aberrators whose optical transformation properties can be represented by a complex multiplicative phase factor, exp[i.phi.(x,y)], where .phi.(x,y) characterizes the optical distortion produced by the thin aberrator. The optical transformation property of an arbitrary distorting medium (i.e., a "thick" aberrator), however, cannot be adequately described simply by a multiplicative phase factor. In an arbitrary distorting medium characterized by a four-dimensional kernel h(x,y; x.sub.0 y.sub.0), where (x.sub.0,y.sub.0) are the object coordinates and (x,y) are the image coordinates, an input object f(x.sub.0,y.sub.0) results in an output distribution g(x,y) given by: EQU g(x,y)=.intg..intg.f(x.sub.0,y.sub.0) h(x,y; x.sub.0,y.sub.0) dx.sub.0 dy.sub.0.
The approaches and approximations used for representing the optical transformation properties of thin phase distorters (i.e., where the effective optical thickness of the aberrator is less than approximately the wavelength of the light) have been shown to be inadequate for characterizing thick aberrators. Therefore, new methods of determining optical transformation properties of arbitrary distorting media are needed for reconstructing high-resolution images of two-dimensional information transmitted through thick aberrators.